The audio coding and decoding technology is the core of multimedia application technologies such as digital audio broadcast, music transmission and audio telecommunication in the internet and so on, which will greatly benefit from the improvement of the pressing performance of audio encoders. A perceptual audio encoder, one kind of lossy transform domain coding, is a main modern audio encoder. The existing codec, such as Motion Picture Experts Group (MPEG) 4 Advanced Audio Coding (AAC) and so on, performs transform-domain audio coding and decoding in a non-uniform scalar quantization way, for which the calculation has a high complexity, and the compressing ability is not high. The convention statistical vector quantizer (for example, the vector quantizer designed with LBG algorithm, wherein, the LBG is a vector quantization method provided by Linde, Buzo and Gray) has a strong compressing ability, and therefore has been widely used in audio and video compressing field. However, the calculation complexity of a vector quantizer increases exponentially with the dimension, and the code book obtained by training the training sequence with a clustering algorithm is usually not the global optimal. Recently, a new audio coding and decoding vector quantizer i.e. lattice vector quantization arises, which quantizes signals with lattice points in space grid being the vector quantizer. Since the space lattice points are regular, the code book can be constructed by algebra method and only occupies little storage space, and the lattice vector quantization has the advantages of low calculation complexity and high quantization precision. However, since the existing lattice vector quantization based audio codec (such as G.719 and so on) adopts a sphere grid with respect to the coding and decoding code book, the code book truncation is only applicable to information sources of uniform allocation and Gaussian allocation, and has not a good effect for the voice which is an information source complying with Laplace allocation. Meanwhile, the bit step length of the existing lattice vector quantizer (such as G.719) is integer bits (for example, one bit) during coding, so the step length is too long in low bit allocation, which causes a too concentrated bit allocation and the limited bits can not be used more efficiently; in addition, the grid code book of a single bit of the codec occupies too much storage space.